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Inverse Jacobi multipliers

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Abstract

Inverse Jacobi multipliers are a natural generalization of inverse integrating factors ton-dimensional dynamical systems. In this paper, the corresponding theory is developed from its beginning in the formal methods of integration of ordinary differential equations and the “last multiplier” of K. G. Jacobi. We explore to what extent the nice properties of the vanishing set of inverse integrating factors are preserved in then -dimensional case. In particular, vanishing on limit cycles (in restricted sense) of an inverse Jacobi multiplier is proved by resorting to integral invariants. Extensions of known constructions of inverse integrating factors by means of power series, local Lie Groups and algebraic solutions are provided for inverse Jacobi multipliers as well as a suitable generalization of the concept to systems with discontinuous right-hand side.

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Authors and Affiliations

  1. CONICET Departamento de Matemática Facultad de Ciencias Exactas, Ing. y Agrim., Universidad Nacional de Rosario, Av. Pellegrini 250, 2000, Rosario, Argentina

    Lucio R. Berrone

  2. Laboratoire de Mathématique et Physique Théorique C.N.R.S. UMR 6083, Faculté des Sciences et Techniques Université de Tours Parc de Grandmont, 37200, Tours, France

    Hector Giacomini

Authors
  1. Lucio R. Berrone
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  2. Hector Giacomini
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Berrone, L.R., Giacomini, H. Inverse Jacobi multipliers. Rend. Circ. Mat. Palermo 52, 77–130 (2003). https://doi.org/10.1007/BF02871926

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